High pressure produced-low density polyethylene (LDPE) has excellent processability and is widely used as processed in the form of tubes, pipes, sheets and films. On the other hand, copolymers of ethylene and an .alpha.-olefin having 3 to 12 carbon atoms have a linear molecular structure and a density of 0.945 g/cm.sup.3 or less and are known as linear low density polyethylene (LLDPE), and are obtained by copolymerization in the presence of a Ziegler catalyst system comprising a solid catalyst component containing magnesium and titanium, and an organoaluminum compound or a catalyst system comprising an organic transition metal compound containing a cyclopentadienyl derivative, and a compound capable of reacting with the organic transition metal compound to form an ionic complex and/or an organometallic compound. Although such a linear low density ethylene-.alpha.-olefin copolymer is superior to high pressure produced-low density polyethylene (LDPE) in break strength, it has a higher melt shear viscosity and much poorer processability than LDPE, with the melt flow rate (hereinafter abbreviated as "MFR") being equal. Additionally, it has a very small elongational viscosity and a small melt tension. In order to overcome these problems, the copolymer has been used as a polyblend with LDPE, but the polyblend does not always exhibit a good balance between processability and physical properties, and blending incurs cost.
In order to solve the problems, it has been a practice widely followed to modify the copolymer by reaction with a radical generator, chiefly an organic peroxide, to improve melt tension. However, since the conventional linear low density ethylene-.alpha.-olefin copolymer has a distribution of degree of branching and also has a somewhat wide molecular weight distribution, if the reaction is carried out to such a degree as to attain sufficiently improved melt tension, gelation occurs frequently during processing to cause surface roughening, resulting in only a product of no practical use.
On the other hand, it is known that conventional polyolefin resins are markedly difficult to process by calendering because they are sticky to the calender roll. The sticking of the polyolefin to the roll is considered attributed to low molecular weight components contained in the resin. To prevent this, it has been proposed to add a metallic soap to an olefin resin as disclosed in JP-A-7-26077 (unexamined published Japanese patent application). However, addition of a metallic soap to a resin not only causes contamination of the roll more or less but is also unfavorable from the hygienic consideration.